It’s simply not the case that religious morality comes from religion. Morality comes from culture, continuously iterated on and negotiated by its members. Should we really believe that no one was honest, kind, or merciful before Muhammad? Of course not, those were already virtues, and they were included in his teachings because they are virtues. Even idiosyncratic moral obligations like keeping halal/kosher derive from the pre-religious situation of the people among whom the religion developed – for example, pork was forbidden in part because pigsties were located beneath outhouses, and were fed on human waste.
Religious morality takes a description of such a morality and tries to fix it in place for all time. A culturally-negotiated code from a culture that no longer exists, applied out of time and reason, to a culture with different needs. Thankfully, the attempt mostly fails; societies ostensibly practicing the same religion enact it differently, and maintain moral codes as different as many between different religions. And none apply it in the way it was applied in the ancient culture of its origin, because ancient cultures and modern cultures face different moral questions. The Quran condoned slavery, but today no Islamic country permits it, and only extremist groups like ISIS and Boko Haram continue to follow the fixed code of the Quran.
So what is the basis for Humanist morality? The same thing as is the basis for religious morality: the continuous iteration and negotiation of human beings. The difference is that it is not limited to what can be tortured from an ancient text. Humanist morality is what we get when we consider the place of the human species today, what we have and are capable of, who our neighbors are, and what behaviors make sense in this context. That’s why it so successfully leads religions away from their ancient codes.
Similarly, a Humanist continues to live for the same reason a religious person does: self-preservation is an instinct, we value our lives because those humans who did not tended not to produce the humans alive today. The typical human does not need reason to justify continuing to live, any more that we need reason to justify the taste of honey. The lack of a will to live is a symptom used to diagnose depression (and I have to think that would apply equally to someone who only continued to live out of a fear of divine retribution).
Granted, Humanism would not consider suicide a moral wrong. For most Humanists, our bodily autonomy and right to self-determination would include the right to end ones life. I regard suicide as tragic, something to be avoided in virtually all cases, and would try to help someone to choose differently. But it is their choice.
This is a strange selective focus. The vast majority of fathers and sons do not need a prohibition against father-son incest to prevent them from engaging in it, and again I would suggest that if the only reason a person is refraining from father-son incest is fear of divine retribution, that would be considered a symptom of mental illness. And moral edge cases don’t tell us much about moral systems; it’s a literal mathematical impossibility for a system of rules to cover every possible case, so the ability to handle strange and unlikely cases is just not informative. Not to mention, it lends itself to prurient hypotheticals, chosen for emotional effect rather than evidentiary weight.
But, you need an answer, so I will answer:
First, a child cannot consent. Humanism values consent because it values individual freedom, and one way to protect freedom for everyone is to require that they are willing participants in their lives. In children, we often don’t require their consent, but only in cases where something is being done in the child’s interest and the child is not capable of understanding that it is good. That’s not the case in father-son incest. There, the father would be using the son for his own benefit, and the son does not benefit, likely suffers, and cannot consent. So if the son is a child, we should not permit father-son incest.
Similar motivations justify prohibiting incest between a father and his adult son. As you so graphically illustrate, the possibility of a future sexual relationship can interfere with a father’s obligations to his children, making choices not for the benefit of the child, but to increase the likelihood of the child later accepting a sexual advance. Because so much of parenting happens behind closed doors, such an outcome is presumptively improper, and a prohibition on a later relationship will serves to discourage the present mistreatment of the child.
But suppose a child was adopted from birth and never knew his father, was raised in a kind and loving household by devoted parents, grew to be an intelligent and independent adult with one or more loving sexual experiences with peers, and only then met his father and developed a consensual relationship with him. In that case, other than the efficiency of simpler laws, it does not seem there would be any reason to prohibit it: they are consenting adults, they can do as they please with their own bodies. They may face social repercussions due to how their behavior makes others feel, but our feeling of distaste does not make their actions immoral.
And, though I repeat myself: I would feel no less disgust if, though they badly wished they could consummate their desire for each other, they refrained because of a fear of divine retribution.